Finite Group Databasebeta

← #14763104

Subgroups — #14763104

Order 2816.

1374 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic
2C2×#10622446C211yesmaximal, characteristic, complemented
3#13071012C211yesmaximal, characteristic, complemented
4#13069543C211yesmaximal, characteristic, complemented
5#13069542C211yesmaximal, characteristic, complemented
6#13069540C211yesmaximal, characteristic, complemented
7#13069424C214yesmaximal, complemented
8#13068555C214yesmaximal, complemented
9C11×#1981C211yesmaximal, characteristic, complemented
10C22×#4343C2212yes—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#67000C2212yes—
13#10623256—24no—
14#10623256C418yescomplemented
15C2×#66948—21no—
16C2×#66948—21no—
17C2×#66946—21no—
18C2×#66946—21no—
19C2×#66927C2211yescharacteristic
20C2×C42×D11C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2214yes—
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66899C2214yes—
25C2×#66885C2214yes—
26C2×(C2×D11)⋊C8C2212yes—
27C2×C8×Dic11C2212yes—
28#10622600C2212yes—
29#10622590C2212yes—
30C2×#66873C2214yes—
31C4×(C2×D11)⋊C4—21no—
32C4×C4⋊Dic11C2211yescharacteristic
33#10622545—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35#10622446—24no—
36#10622277—21no—
37#10622264—21no—
38C22×Q8×C11C2312yes—
39C2×#4343—24no—
40C2×#4343—44no—
41C2×#4343—44no—
42C2×#4343C2×C418yes—
43C22×D44—22no—
44C22×D44—21no—
45C22×D44—21no—
46C22×D44C2312yes—
47C22×C4×D11—22no—
48C22×C4×D11D411yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×C4×D11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8C2×C414yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59#67000—24no—
60#67000C2×C418yes—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×C4⋊Dic11C2312yes—
65C2×C4×Dic11—21no—
66C2×C4×Dic11D411yescharacteristic
67C2×C4×Dic11D411yescharacteristic
68C2×C4×Dic11C2311yescharacteristic
69C22×C11⋊C8C2312yes—
70#66948—28no—
71#66948—28no—
72#66946—28no—
73#66946—28no—
74#66927—22no—
75#66927C2×C414yes—
76C42×D11C2×C414yes—
77C42×D11D414yes—
78C11×C4⋊C8—22no—
79C11×#103—44no—
80C11×#95—21no—
81#66899—44no—
82C11⋊#95—21no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86#66885—44no—
87(C2×D11)⋊C8—24no—
88C8×Dic11—24no—
89#66873—44no—
90C4⋊(C11⋊C8)—22no—
91#21807—111nomaximal, Sylow
92C23×D11—22no—
93C23×D11C2×D411yescharacteristic
94C2×Q8×C11—22no—
95C2×Q8×C11—24no—
96C2×Q8×C11—24no—
97C2×Q8×C11C22×C414yes—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—22no—
104C22×Dic11C2×D411yescharacteristic
105C22×Dic11C2×D411yescharacteristic
106C22×Dic11C2×D411yescharacteristic
107#4343—416no—
108#4343—48no—
109#4343—48no—
110C2×D44—28no—
111C2×D44—24no—
112C2×D44—24no—
113C2×D44—22no—
114C2×D44—24no—
115C2×D44—24no—
116C2×D44—44no—
117C2×D44—48no—
118C2×D44—42no—
119C2×D44—42no—
120C2×D44C22×C414yes—
121C2×C4×D11—28no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—42no—
127C2×C4×D11—48no—
128C2×C4×D11C22⋊C414yes—
129C2×C4×D11C22⋊C414yes—
130C2×C4×D11C22×C412yes—
131C2×C4×D11C2×D412yes—
132C2×C8×C11—22no—
133C2×C8×C11—24no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C42×C11—42no—
139C42×C11C22×C412yes—
140C42×C11C2×D412yes—
141(C2×D11)⋊C4—28no—
142(C2×D11)⋊C4—28no—
143(C2×D11)⋊C4—44no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4×Dic11—42no—
147C4×Dic11C22⋊C414yes—
148C4×Dic11C22⋊C414yes—
149C4×Dic11C22×C412yes—
150C4×Dic11C2×D412yes—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—24no—
153C2×#532—111no—
154C2×#431—111no—
155#2283—111no—
156#1982—111no—
157#1982—111no—
158#1981—111no—
159#1981D1111yescharacteristic, complemented
160#1958—114no—
161#1788—114no—
162C23×C11C22×D411yescharacteristic
163C22×D11—22no—
164C22×D11—21no—
165C22×D11—21no—
166C22×D11—22no—
167C22×D11—24no—
168C22×D11—44no—
169C22×D11—42no—
170C22×D11—42no—
171C22×D11—44no—
172C22×D11C2×C22⋊C412yes—
173Q8×C11—28no—
174Q8×C11—42no—
175Q8×C11—42no—
176C2×C4×C11—22no—
177C2×C4×C11—24no—
178C2×C4×C11—44no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11C2×C22⋊C412yes—
183C2×C4×C11C2×C22⋊C412yes—
184C2×C4×C11#13512yes—
185C2×C4×C11#13512yes—
186C2×C4×C11C23×C411yescharacteristic
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11H(5,𝔽2)12yes—
189C2×C4×C11H(5,𝔽2)12yes—
190C2×Dic11—22no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—22no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11C2×C22⋊C412yes—
198C2×Dic11C2×C22⋊C412yes—
199C2×Dic11C2×C22⋊C412yes—
200D44—28no—
201D44—48no—
202D44—416no—
203D44—42no—
204D44—42no—
205D44—48no—
206C4×D11—24no—
207C4×D11—22no—
208C4×D11—22no—
209C4×D11—28no—
210C4×D11—44no—
211C4×D11—416no—
212C8×C11—42no—
213C11⋊C8—42no—
214C22×#41—112no—
215#532—118no—
216#532—224no—
217C2×C4⋊Q8C2×D1111yescharacteristic
218C2×#127—111no—
219C2×#124—112no—
220C2×#121—221no—
221C2×#121—221no—
222C2×C4×D4—221no—
223C2×C4×D4—221no—
224C22×C42—111no—
225#431—224no—
226C2×C4⋊C8—111no—
227C2×C4⋊C8C2×D1111yescharacteristic
228C2×#103—114no—
229C2×#103C2×D1114yes—
230C2×#102—114no—
231C2×#102—114no—
232C2×C22⋊C8—112no—
233C2×C4×C8—112no—
234#383—221no—
235#382—112no—
236#381—221no—
237#380—112no—
238C4×C4⋊C4—111no—
239C4×C4⋊C4C2×D1111yescharacteristic
240C4×C22⋊C4—221no—
241#376—221no—
242C22×C11C22×C22⋊C411yescharacteristic
243C22×C11#53512yes—
244C22×C11C2×#13511yescharacteristic
245C22×C11C2×#13511yescharacteristic
246C22×C11#57512yes—
247C2×D11—22no—
248C2×D11—22no—
249C2×D11—22no—
250C2×D11—42no—
251C2×D11—42no—
252C2×D11—44no—
253C2×D11—44no—
254C2×D11—44no—
255C2×D11—84no—
256C2×D11—84no—
257C4×C11—22no—
258C4×C11—44no—
259C4×C11—82no—
260C4×C11#41614yes—
261C4×C11#51812yes—
262C4×C11#53511yescharacteristic
263C4×C11#53511yescharacteristic
264Dic11—22no—
265Dic11—22no—
266Dic11—22no—
267Dic11—82no—
268C2×#41—118no—
269C2×#41—224no—
270C2×#41—444no—
271C2×#41—444no—
272C22×Q8C22×D1112yes—
273C22×D4—112no—
274C22×D4—222no—
275C22×D4—221no—
276C22×D4—221no—
277C23×C4—111no—
278C23×C4—111no—
279C23×C4—111no—
280C23×C4—222no—
281C22×C8—112no—
282C22×C8C22×D1112yes—
283C4⋊Q8—22no—
284C4⋊Q8C4×D1114yes—
285#127—114no—
286#127—222no—
287#124—118no—
288#124—224no—
289#121—228no—
290#121—228no—
291C4×D4—228no—
292C4×D4—228no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—112no—
296C2×C4⋊C4C22×D1112yes—
297C2×C22⋊C4—222no—
298C2×C22⋊C4—222no—
299C2×C22⋊C4—222no—
300C2×C42—21no—
301C2×C42—111no—
302C2×C42—111no—
303C2×C42—111no—
304C2×C42—114no—
305C2×C42—114no—
306C2×C42—221no—
307C2×C42C22×D1111yescharacteristic
308C4⋊C8—22no—
309C4⋊C8—222no—
310#103—44no—
311#103—444no—
312#102—444no—
313#102—444no—
314C22⋊C8—224no—
315C4×C8—224no—
316#95—21no—
317#95—222no—
318#95—222no—
319#95—222no—
320#95—221no—
321C2×C11#230911yescharacteristic
322C2×C11C2×#41611yescharacteristic
323C2×C11#289611yescharacteristic
324C2×C11#321212yes—
325C2×C11#321212yes—
326D11—42no—
327D11—84no—
328C24—111no—
329C24—222no—
330#41—4416no—
331#41—448no—
332#41—448no—
333C2×Q8—22no—
334C2×Q8—24no—
335C2×Q8—24no—
336C2×Q8C2×C4×D1114yes—
337C2×D4—114no—
338C2×D4—228no—
339C2×D4—224no—
340C2×D4—224no—
341C2×D4—222no—
342C2×D4—224no—
343C2×D4—224no—
344C2×D4—444no—
345C2×D4—448no—
346C2×D4—442no—
347C2×D4—442no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—111no—
351C22×C4—111no—
352C22×C4—111no—
353C22×C4—114no—
354C22×C4—112no—
355C22×C4—112no—
356C22×C4—114no—
357C22×C4—228no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—442no—
364C22×C4—448no—
365C22×C4D4×D1111yescharacteristic
366C22×C4D4×D1111yescharacteristic
367C22×C4C23×D1111yescharacteristic
368C2×C8—22no—
369C2×C8—24no—
370C2×C8—222no—
371C2×C8—224no—
372C4⋊C4—24no—
373C4⋊C4—24no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—222no—
377C4⋊C4—222no—
378C22⋊C4—228no—
379C22⋊C4—228no—
380C22⋊C4—444no—
381C42—42no—
382C42—114no—
383C42—114no—
384C42—112no—
385C42—112no—
386C42—442no—
387C42C2×C4×D1112yes—
388C42D4×D1112yes—
389C11#2180711yescharacteristic, complemented, Sylow
390C23—112no—
391C23—221no—
392C23—221no—
393C23—222no—
394C23—222no—
395C23—224no—
396C23—442no—
397C23—442no—
398C23—444no—
399C23—444no—
400C23C2×D4×D1111yescharacteristic
401Q8—28no—
402Q8—42no—
403Q8—42no—
404D4—228no—
405D4—448no—
406D4—4416no—
407D4—442no—
408D4—448no—
409D4—442no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—44no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—112no—
417C2×C4—112no—
418C2×C4—112no—
419C2×C4—221no—
420C2×C4—221no—
421C2×C4—222no—
422C2×C4—222no—
423C2×C4—222no—
424C2×C4—224no—
425C2×C4—228no—
426C2×C4—222no—
427C2×C4—444no—
428C2×C4—4416no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4C22⋊C4×D1112yes—
433C2×C4C22⋊C4×D1112yes—
434C2×C4#6696912yes—
435C2×C4#6697212yes—
436C2×C4C22×C4×D1111yescharacteristic
437C2×C4C2×D4×D1111yescharacteristic
438C2×C4#6703712yes—
439C2×C4#6704212yes—
440C8—42no—
441C8—442no—
442C22—222no—
443C22—222no—
444C22—222no—
445C22—442no—
446C22—442no—
447C22—444no—
448C22—444no—
449C22—444no—
450C22—884no—
451C22—884no—
452C22C2×C22⋊C4×D1111yescharacteristic
453C22#1062313812yes—
454C22C2×#6696911yescharacteristic
455C22C2×#6697211yescharacteristic
456C22#1062330812yes—
457C4—22no—
458C4—44no—
459C4—82no—
460C4—222no—
461C4—222no—
462C4—222no—
463C4—882no—
464C4#1062241714yes—
465C4#1062307612yes—
466C4#1062320511yescharacteristic
467C4#1062324611yescharacteristic
468C2—442no—
469C2—884no—
470C2#1307119511yescharacteristic
471C2C2×#1062241711yescharacteristic
472C2#1307713411yescharacteristic
473C2#1307959112yes—
474C2#1307959712yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1981C2
socleC23×C11C22×D4
prime radicalC2×#10623256C2
cosocleC22×C4×C11C24
hypercenter#1981D11
hypocenterC11#21807
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#10622446C2semidirect
3. #13071012C2semidirect
4. #13069543C2semidirect
5. #13069542C2semidirect
6. #13069540C2semidirect
7. #13069424C2semidirect
8. #13068555C2semidirect
9. C11×#1981C2semidirect
14. #10623256C4semidirect
159. #1981D11semidirect
389. C11#21807semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106232562
C2×#106224462
#130710122
#130695432
#130695422
#130695402
#130694242
#130685552
C11×#19812
#2180711